Question

The value of $\cot {15}^{\circ }\cot {20}^{\circ }\cot {70}^{\circ }\cot {75}^{\circ }$ is equal to

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is C $1$

The value of $\cot {15}^{\circ }.\cot {20}^{\circ }.\cot {70}^{\circ }.\cot {75}^{\circ }$ is
$=(\cot {15}^{\circ }.\cot {75}^{\circ })\left(\cot {20}^{\circ }\cot {70}^{\circ }\right)$

Now $\cot {75}^{\circ }=\tan {15}^{\circ }$ and $\cot {70}^{\circ }=\tan {20}^{\circ }$ ....................... $\cot (90-\theta )=\tan \theta$

Therefore, the given expression can be written as
$\left(\cot {15}^{\circ }\tan {15}^{\circ }\right)\left(\cot {20}^{\circ }\tan {20}^{\circ }\right)$
$=1\times 1=1$